The Exact Curve Equation for Majorana Stars

Feng, Yao; Li, Dechao; Liu, Haodi; Fu, Libin; Wang, Xiaoguang

doi:10.1038/s41598-017-15776-w

Cited by 6 publications

(2 citation statements)

References 30 publications

(25 reference statements)

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“…In this article, we employ Majorana stellar representation (MSR) to arrive at a geometric visualization of the topological properties of the quadrupolar subspace. MSR is an old idea due to Ettore Majorana [10] which has gained prominence recently as a tool to understand geometric properties of finite-dimensional Hilbert spaces [11][12][13][14][15][16][17][18][19][20] and their connection to entalgement properties of permutation symmetric states of spin half system. The original idea of Majorana has also been extended to permutation symmetric states of higher spin systems [21].…”

Section: Introductionmentioning

confidence: 99%

Topology of quadrupolar Berry phase of a Qutrit

Singh¹,

Karn²,

Bhowmick³

et al. 2023

Preprint

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We examine Berry phase pertaining to purely quadrupolar state ( ψ| S|ψ = 0) of a spin-1 system. Using the Majorana stellar representation of these states, we provide a visualization for the topological (zero or π) nature of such quadrupolar Berry phase. We demonstrates that the π Berry phase of quadrupolar state is induced by the Majorana stars collectively tracing out a closed path (a great circle) by exchanging their respective positions on the Bloch sphere. We also analyse the problem from the perspective of dynamics where a state from the quadrupolar subspace is subjected to a static magnetic field. We show that time evolution generated by such Hamiltonian restricts the states to the quadrupolar subspace itself thereby producing a geometric phase (of the Aharonov-Anandan type) quantized to zero or π. A global unitary transformation which maps the quadrupolar subspace to the subspace of purely real states proves a natural way of understanding the topological character of this subspace and its connection to the anti-unitary symmetries.

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Section: Introductionmentioning

confidence: 99%

Topology of quadrupolar Berry phase of a Qutrit

Singh¹,

Karn²,

Bhowmick³

et al. 2023

Preprint

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“…Consequently, this representation becomes an efficient method to study the geometric related properties of multipartite or high-dimensional state such as entanglement [2][3][4][5][6][7][8][9][10][11], Berry phase [12][13][14][15][16][17][18], as well as their dynamics, geometric structures and response to geometric transformations (e.g. rotations and inversions) [19][20][21][22][23][24][25][26][27][28][29]. By using MR, entanglement, and Berry phase for symmetric multi-qubit states can be related to each other and intuitively represented by the trajectories and distributions of the stars on the Bloch sphere [16,18,30].…”

Section: Introductionmentioning

confidence: 99%

Majorana decomposition for two-qubit pure states

Yang¹,

Liu²,

Fu³

2021

J. Phys. A: Math. Theor.

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The Majorana representation (MR), which represents a quantum state and its evolution with the Majorana stars (MSs) on the Bloch sphere, provides us an intuitive way to study symmetric multiqubit pure states physical system with SU(2) symmetry. In this work, we propose a method to extend the MR for generic two-qubit pure states. By adding an additional reference star (RS), which represents the symmetry of the qubits, on the symmetric two qubit state with two base stars, we give a more general MR for both symmetric, anti-symmetric and generic two-qubit states. Using this method, we study the entanglement, Berry phase and their relation by this Majorana decomposition. Furthermore, the symmetries for different type of two-qubit states are also discussed via the RSs and correlation between the two MSs.

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Majorana Representation for a Composite System

Yang

Zhang

2021

Int J Theor Phys

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The Exact Curve Equation for Majorana Stars

Cited by 6 publications

References 30 publications

Topology of quadrupolar Berry phase of a Qutrit

Topology of quadrupolar Berry phase of a Qutrit

Majorana decomposition for two-qubit pure states

Majorana Representation for a Composite System

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